fixed a bug causing "c" (the scaling factor) to be calculated incorre…

…ctly. This bug was caused by a typo introduced in v1.3.0 (commit 91d30b8) when converting the for-loops into compact numpy expressions.

README.md

@@ -31,7 +31,7 @@ Superpose3D() takes two lists (or numpy arrays) of xyz coordinates
 ("clouds", **X** and **x**).
 Treating them as rigid objects, "Superpose3D()" attempts to superimpose
 them using **rotations**, **translations**,
-~~and (optionally) **scale** transformations~~
+and (optionally) **scale** transformations
 in order to minimize the root-mean-squared-distance (RMSD)
 between corresponding points from either cloud, where RMSD is defined as:
 
@@ -82,13 +82,11 @@ R. Diamond, (1988)
 "A Note on the Rotational Superposition Problem",
  Acta Cryst. A44, pp. 211-216.
 
-### Scale transformations <-- NOT WORKING (2022-3-07)
+### Scale transformations
 
-***Note: The scale transformation feature described below [does not work](https://github.com/jewettaij/superpose3d/issues/3). Please ignore the next paragraph. This will get fixed soon. -Andrew 2022-3-07.***
+This version has been augmented slightly to support scale transformations.  (I.E. multiplication by scalars.  This can be useful for the registration of two different annotated volumetric 3-D images of the same object taken at different magnifications.)
 
-~~This version has been augmented slightly to support scale transformations.  (I.E. multiplication by scalars.  This can be useful for the registration of two different annotated volumetric 3-D images of the same object taken at different magnifications.)~~
-
-~~Note that if you enable scale transformations (i.e. if *allow_rescale=True*), you should be wary if the function returns a negative **c** value.  Negative **c** values correspond to inversions (reflections).  For this reason, if you are using this function to compare the conformations of molecules, you should probably set *allow_rescale=False*.  This will prevent matching a molecule with its stereoenantiomer.~~
+Note that if you enable scale transformations (i.e. if *allow_rescale=True*), you should be wary if the function returns a negative **c** value.  Negative **c** values correspond to inversions (reflections).  For this reason, if you are using this function to compare the conformations of molecules, you should probably set *allow_rescale=False*.  This will prevent matching a molecule with its stereoenantiomer.
 
 ## Installation using pip
 

superpose3d/__init__.py

@@ -10,6 +10,7 @@
 
 import numpy as np
 from numpy import linalg as LA
+from math import *
 
 def Superpose3D(aaXf_orig,   # <-- coordinates for the "frozen" object
                 aaXm_orig,   # <-- coordinates for the "mobile" object
@@ -183,13 +184,12 @@ def Superpose3D(aaXf_orig,   # <-- coordinates for the "frozen" object
         WaxaiXai = 0.0
         for a in range(0, N):
             for i in range(0, 3):
-                Waxaixai += aWeights[a] * aaXm[a,i] * aaXm[a,i]
-                WaxaiXai += aWeights[a] * aaXm[a,i] * aaXf[a,i]
+                Waxaixai += aWeights[a,0] * aaXm[a,i] * aaXm[a,i]
+                WaxaiXai += aWeights[a,0] * aaXm[a,i] * aaXf[a,i]
         """
         # new code (avoiding for-loops)
-        Waxaixai = np.sum(aWeights * aaXm ** 2)
-        WaxaiXai = np.sum(aWeights * aaXf ** 2)
-
+        Waxaixai = np.sum(aWeights * aaXm * aaXm)
+        WaxaiXai = np.sum(aWeights * aaXm * aaXf)
         c = (WaxaiXai + pPp) / Waxaixai
 
     # Finally compute the RMSD between the two coordinate sets: